I had looked this up at one time, but have forgotten which one. I think it was one of the forgettable ones between Lincoln and TR.
If I remember correctly, his mom moved across the border from Canada when quite young. I couldn't find any information on naturalization proceedings, and I'm not sure there was much in the way of a formal process during most of the 19th century.
I do know that in the early part of the century a woman automatically took her husband's citizenship when she married, so it may not have been relevant anyway. I believe during the first part of the 19th only the father's status was considered when determining citizenship. As women acquired more rights as individuals over the course of the century this changed, but I'm vague on dates for specific changes.